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We analyze a simultaneous continuous measurement of photon-counting andhomodyne detection. The stochastic master equation or stochastic Schr\"odingerequation describing the measurement process includes both jump-type anddiffusive-type stochastic increments. Analytic expressions of the wave functionconditioned on homodyne and photon-counting records are obtained, yielding theprobability density distributions and generating functions of the measurementrecords. Formula for the expectation values of the homodyne records conditionedon a photon-counting event is also derived which quantitatively describes themeasurement backaction of photon-counting on the homodyne output. The obtainedresults are applied to typical initial states --- coherent, number, thermal,and squeezed states. Monte Carlo simulations of the measurement processes arealso presented to demonstrate the dynamics of the combined measurement process.

journal of physics. a, mathematical and theoretical

Simultaneous continuous measurement of photon-counting and homodyne  detection on a free photon field: dynamics of state reduction and mutual  influence of measurement backaction